A difficulty which is common in fantasy football is choosing between two players who seem to offer similar potential for points. Choosing between two goalkeepers is the most simple example of this, as there are only two choices, and clear odds available for clean sheet/goals conceded/bookings available.
This week I have to choose between Ben Foster who has a double gameweek of WBA (H) and EVE (A), or Joe Hart who has a single gameweek of WIG (H). A question I have often seen asked is whether to go for a player who offers a good chance of a return in a single week (Hart in this example, with odds of 1.96 of a clean sheet on Betfair) or a double gameweeker who offers more doubtful returns in terms of points in each game, but should rack points up by virtue of playing both (Foster in this example, with odds of around 3.05 and 6.4 respectively).
In terms of calculating the likelihood of Foster getting at least one, or two clean sheets, well thats a bit of GCSE maths, so I won't bother for now, as there are other things that determine how many points he is likely to score, such as goals conceded, minutes played, saves, bonus, bookings and penalty saves.
Goals conceded is another simple one, and odds are readily available (I'm using Betfair ones as they don't include an over-round, i.e. what bookies make their money on). Minutes played is more difficult, but given there is no injury news, and he has played a full 90 minutes in every game this season, we can assume that this is by far the most likely outcome, with a small chance of him becoming injured before the game (0.01) and a small chance of becoming injured during (0.02, spread evenly across the 90 minutes). Saves is even more difficult, and for now, I'm basing it on the distribution shown in Birmingham's previous games this season (which looks something like a right-shifted poisson distribution, with a peak at 3 saves). Bonus is more likely to be awarded where there have been a high number of saves, or a penalty saves, and is therefore modelled on this. Bookings and Penalty saves are from betfair odds again.
Using Monte Carlo Simulation (e.g. http://www.projectsmart.co.uk/docs/monte-carlo-simulation.pdf , simpler than it sounds!), I modelled the likelihood of each possible number of points for both of the goalkeepers, based on the probabilities described above. Probability is on the y-axis, game points on the x-axis.
So there are some conclusions we can draw from this; the most likely outcome (~30%) for Joe Hart is a score of seven points (this is predominantly made up of games where he keeps a clean sheet, with between 3 and 5 saves), followed by three points (~20%) (predominantly where he concedes a single goal, but makes between 3 and 5 saves). Ben Foster's probabilities are more interesting, the distribution unsurprisingly being much more flat and widespread, due to being produced by two games. The most likely outcome for Ben is a score of five points (~15%), (made up of several outcomes, the most common of which being not keeping a clean sheet in either game, but making between 3 and 5 saves in one of them). However, Foster's average score is higher than Hart's, a mean of around 7.3, versus Joe's measly 5.2.
So, even though Foster is less likely to gain clean sheets than Hart, the points gained from extra saves and minutes played mean that Foster's average score is higher. Then there's always the slim possibility of a whopping two clean sheets (~4%) with some bonus on top. Which is what we live for as Fantasy managers, isn't it?
